91Ó°ÊÓ

Using set notation, write out the sample space for each of the following random experiments. (a) A coin is tossed three times in a row. The observation is how the coin lands ( \(H\) or \(T\) ) on each toss. (b) A basketball player shoots three consecutive free throws. The observation is the result of each free throw \((s\) for success, \(f\) for failure). (c) A coin is tossed three times in a row. The observation is the number of times the coin comes up tails. (d) A basketball player shoots three consecutive free throws. The observation is the number of successes.

Using set notation, write out the sample space for each of the following random experiments. (a) A coin is tossed four times in a row. The observation is how the coin lands ( \(H\) or \(T\) ) on each toss. (b) A student randomly guesses the answers to a fourquestion true-or-false quiz. The observation is the student's answer ( \(T\) or \(F\) ) for each question. (c) A coin is tossed four times in a row. The observation is the percentage of tosses that are heads. (d) A student randomly guesses the answers to a fourquestion true-or-false quiz. The observation is the percentage of correct answers in the test.

Using set notation, write out the sample space for each of the following random experiments: (a) Roll three dice. The observation is the total of the three numbers rolled. (b) Toss a coin five times. The observation is the difference (# of heads-# of tails) in the five tosses.

Using set notation, write out the sample space for each of the following random experiments: (a) Three runners \((A, B,\) and \(C\) ) are running in a race (assume that there are no ties). The observation is the order in which the three runners cross the finish line. (b) Four runners \((A, B, C,\) and \(D)\) are running in a qualifying race (assume that there are no ties). The top two finishers qualify for the finals. The observation is the pair of runners that qualify for the finals.

You reach into a large jar containing jelly beans of four different flavors [Juicy Pear \((J),\) Kiwi \((K),\) Licorice \((L),\) and Mango ( \(M\) ) ] and grab two jelly beans at random. The observation is the flavors of the two jelly beans. Using set notation, write out the sample space for this experiment.

The sample spaces are too big to write down in full. In these exercises, you should describe the sample space either by describing a generic outcome or by listing some outcomes and then using the ... notation. In the latter case, you should write down enough outcomes to make the description reasonably clear. A student randomly guesses the answers to a multiplechoice quiz consisting of 10 questions. The observation is the student's answer \((A, B, C, D,\) or \(E)\) for each question. Describe the sample space.

A student randomly guesses the answers to a four-question true-or-false quiz. The observation is the student's answer (T or \(F\) ) for each question [see Exercise \(2(\mathrm{~b})\) ]. Write out the event described by each of the following statements as a set. (a) \(E_{1}:\) "the student answers \(T\) to two out of the four questions." (b) \(E_{2}\) : "the student answers \(T\) to at least two out of the four questions." (c) \(E_{3}\) : "the student answers \(T\) to at most two out of the four questions." (d) \(E_{4}:\) "the student answers \(T\) to the first two questions."

A card is drawn out of a standard deck of 52 cards. Each card can be described by giving its "value" \((A, 2,3,4, \ldots,\) \(10, J, Q, K)\) and its "suit" ( \(H\) for hearts, \(C\) for clubs, \(D\) for diamonds, and \(S\) for spades). For example, \(2 D\) denotes the two of diamonds and \(J H\) denotes the jack of hearts. Write out the event described by cach of the following statements as a set. (a) \(E_{1}:\) "draw a queen." (b) \(E_{2}:\) "draw a heart." (c) \(E_{3}:\) "draw a face card." (A "face" card is a jack, queen, or king.)

A coin is tossed 10 times in a row. The observation is how the coin lands ( \(H\) or \(T\) ) on each toss (see Exercise 7 ). Write out the event described by each of the following statements as a set. (a) \(E_{1}:\) "none of the tosses comes up tails." (b) \(E_{2}:\) "exactly one of the 10 tosses comes up tails" (c) \(E_{3}\) : "nine or more of the tosses come up tails."

Five candidates \((A, B, C, D,\) and \(E)\) have a chance to be selected to be on American Idol. Any subset of them (including none of them or all of them) can be selected. The observation is which subset of individuals is selected. Write out the event described by each of the following statements as a set. (a) \(E_{1}:\) "two candidates get selected." (b) \(E_{2}:\) "three candidates get selected." (c) \(E_{3}:\) "three candidates get selected, and \(A\) is not one of them."